在桑尼科夫的委托代理问题中是否存在“黄金降落伞”？
Is there a Golden Parachute in Sannikov's principal-agent problem?
摘要：
本文提供了一个完整的审查连续时间最优承包问题介绍了Sannikov，在扩展的背景下，允许可能不同的贴现率为双方。代理人的问题是寻求最佳的努力，给定的补偿方案提出的委托人在一个随机的地平线。然后，给定最优代理人的响应，委托人根据连续支付、退休和退休时的一次性支付来确定最佳补偿方案。黄金降落伞是一种情况，代理人在某个正停止时间停止任何努力，然后收到付款，可能是一次性付款或连续付款的形式。我们表明，黄金降落伞只存在于某些特定的情况下。这与Sannikov声称的结果相反，Sannikov声称的唯一要求是积极代理人的边际努力成本为零。也就是说，我们表明，没有黄金降落伞，如果这个参数太大。类似地，在凹边际效用的情况下，如果代理人的效用函数在零处具有太负的曲率，则不存在黄金降落伞。在一般情况下，我们证明了一个代理与积极的保留效用是从来没有退休的主要，或退休以上的一些给定的阈值（如在Sannikov的解决方案）。我们发现，不同的贴现因子诱导一个整容的效用函数，它允许减少分析的设置类似于相等的贴现率之一。最后，我们还证实，一个小的保留效用的代理人可能有一个信息租金，这意味着委托人最优地提供给他一个合同，严格高于他的参与价值的效用。
英文摘要：
This paper provides a complete review of the continuous-time optimal contracting problem introduced by Sannikov, in the extended context allowing for possibly different discount rates for both parties. The agent's problem is to seek for optimal effort, given the compensation scheme proposed by the principal over a random horizon. Then, given the optimal agent's response, the principal determines the best compensation scheme in terms of running payment, retirement, and lump-sum payment at retirement. A Golden Parachute is a situation where the agent ceases any effort at some positive stopping time, and receives a payment afterwards, possibly under the form of a lump sum payment, or of a continuous stream of payments. We show that a Golden Parachute only exists in certain specific circumstances. This is in contrast with the results claimed by Sannikov, where the only requirement is a positive agent's marginal cost of effort at zero. Namely, we show that there is no Golden Parachute if this parameter is too large. Similarly, in the context of a concave marginal utility, there is no Golden Parachute if the agent's utility function has a too negative curvature at zero. In the general case, we prove that an agent with positive reservation utility is either never retired by the principal, or retired above some given threshold (as in Sannikov's solution). We show that different discount factors induce a face-lifted utility function, which allows to reduce the analysis to a setting similar to the equal discount rates one. Finally, we also confirm that an agent with small reservation utility may have an informational rent, meaning that the principal optimally offers him a contract with strictly higher utility than his participation value.
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